1. Field of the Invention
A method is disclosed for extrapolating the seismic wavefront traveltimes across ray-path shadow zones due to severe velocity discontinuities found in association with complex geology such as salt domes and the like.
2. Discussion od Relevant Art
In one form of geophysical exploration for natural resources, a seismic wavefield is radiated from a source point at or near the surface of the earth. Initially propagating as a spherically expanding wavefront, the radiation insonifies the various earth layers which usually offer an acoustic impedance mismatch at the layer boundaries due to variations in rock density and acoustic velocity. The wavefield is reflected from the respective layer boundaries to return to the surface where the mechanical earth motions due to the reflected wavefield are converted to electrical signals by transducers. The signals which comprise the seismic data, are stored on archival storage media for future processing.
It is the object of seismic studies to produce a model of a volume of subsurface earth formations in a region of geological and/or economic interest. For an isotropic horizontal stratum with constant velocity, the elapsed time between wavefield emission and wavefield reception at a receiver near the source, multiplied by half the average velocity, is the depth of the incident point of the reflected wavefield on the stratum that lies directly beneath the midpoint between the source and receiver.
If a reflector is tilted or the velocity is spatially variable, that simple relationship no longer holds; the incident point is shifted laterally up-dip relative to the source/receiver midpoint. Proper mapping of dipping or tilted reflectors, requires migration of the wavefields originating from those dipping strata. One well-known migration technique is Kirchhoff depth migration.
The computation of wavefield travel times at selected output points is a key element in successful Kirchhoff depth migration of seismic data. For complex geology, wavefield travel times to the output points are preferably generated by ray tracing from the source. Ray-traced travel-time generation methods are preferred because they can produce travel times for all wavefront arrivals at an output point.
By way of review, a velocity model of a region of interest is provided in FIG. 1. A first ray is shot at a first selected angle from a source into a velocity model. The ray is traced through all of the intervening earth layers via pathways determined by the well-known Snell's-law refraction effects at the velocity discontinuities that characterize the layer boundaries. Given the velocity sequence which is known from the velocity model, the travel time of the wavefront of a radiated wavefield may be computed at any point along the ray path. A second and additional rays, directed at second and additional selected angles relative to the surface are shot from the source. A wavefront envelope at any given instant, for use in migration, can be reconstructed by joining the loci corresponding to equal travel times as measured along the respective ray segments. By definition, the wavefront is perpendicular to the ray trajectory.
One method is taught by U.S. Pat. No. 5,229,938, issued Jul. 20, 1993 to Shein-Shen Wang et al. Here is taught a method for obtaining two-way travel times for source and receiver pairs that includes the steps of determining a set of one way travel times for each source to a plurality of image points and a set of one way travel times for each receiver to a plurality of image points. Ray sets are generated for both sources and receivers. Travel times from a source position to image points are computed by two-point interpolation using the ray sets. Two-way travel time is computed by summing two sets, one set each for the source and receiver positions. A two-way travel time set is obtained for a particular source and receiver combination for all imaging points.
In general, for prestack depth imaging, Kirchhoff migration is preferred. Kirchhoff migration requires use wavefront travel time generators of any one of several well-known types that are based on ray tracing as above outlined. Ray-tracing methods are useful in complex geological structures but they produce unwanted shadow zones in the travel-time data in the presence of complex stratigraphic velocity domains. It is assumed, of course that the shadow zones are not the result of penury in ray-path shooting. Ray-traced traveltimes permit use of both first-arrival data as well as maximum-energy arrivals, which latter data produce superior imagery. However those methods are very slow and greedy of computer processing time.
Eikonal (finite difference) traveltime generators are very fast and do not produce shadow zones. Finite difference traveltime generators will always pick the first arrival travel times whereas with ray-traced travel-time generators, the desired portion of the wave front must specifically be selected.
A well-known finite-difference traveltime generator is disclosed in a paper published in the Bulletin of the Seismological Society of America, v. 78, n. 6, December 1988, pp 2062-2076, by John Vidale. Here the travel times of the first arriving seismic waves through any velocity structure can be rapidly computed on a multi-dimensional grid by finite-difference point-to-point extrapolation. Wavefronts are tracked instead of rays. Refracted waves are properly treated and shadow zones are filled the appropriate wavefront segments. This scheme is very fast and is useful in tomographic inversion and Kirchhoff migration in geologic section characterized by smooth lateral velocity gradients.
In accordance with this invention, a hybrid traveltime generator is proposed for use in the presence of a complex velocity model wherein wavefronts initially will be generated using any well-known wavefront travel-time generator. Upon encountering a wavefront shadow zone the Vidale finite-difference wavefront generator will be used for extrapolating the wavefronts across missing wavefronts in wavefront shadow-zones.